AE 201 – Spring 2025
Problem Set 7
1. (10 pts) A popular technique engineers and researchers use for solving really difficult problems is called brainstorming, which can sometimes result in what are called “wild ideas.” If
you are asked to lead a brainstorming session for the AIAA Design, Build & Fly team, write
down some of the things you might do to prepare for and then conduct this session, and how
you would deal with any wild ideas that come up.
2. (10 pts) Given the information in the table below, determine whether the flows about the two
geometrically similar airfoils are dynamically similar.
Airfoil 1
α1 = 5◦
V1 = 210 m s−1
ρ1 = 1.2 kg m−3
µ1 = 1.8 × 10−5 kg m−1 s−1
a1 = 300 m s−1
c1 = 1.0 m
Airfoil 2
α2 = 5◦
V2 = 140 m s−1
ρ2 = 3 kg m−3
µ2 = 1.5 × 10−5 kg m−1 s−1
a2 = 200 m s−1
c2 = 0.5 m
3. (10 pts) Consider the steady flow of a particular gas through a horizontal, converging pipe
that has an inlet diameter of 0.21 m and an outlet diameter of 0.15 m. The density of the gas
is known to change from 0.92 kg/m3 at the inlet to 0.82 kg/m3 at the outlet. If the inlet flow
velocity of the gas is 4.9 m/s, what is its exit velocity? Hint: Assume one-dimensional flow.
4. (10 pts) A gas of density 0.92 kg/m3 flows through a pipe with a volume flow rate of
0.31 m3 /s. As shown in the figure below, the pipe has an inlet section diameter of 23 cm
and an outlet section diameter of 11 cm. A water manometer measures the pressure difference between the inlet and outlet sections. Assuming an ideal incompressible fluid flow,
calculate the height h on the manometer. Also calculate the force on the pipe.
5. (10 pts) A horizontal water jet with diameter d = 4 cm impacts on a inclined plate. Using
the conservation equations, find the force, ~F, on the plate. Be sure to indicate the direction
of the force. Assume one-dimensional incompressible over any cross-section. Also, assume
no losses from viscous effects.
6. (10 pts) Consider the flow-turning block shown below. A circular jet of water with diameter
D j =10 cm at a velocity V j = 13 ms−1 enters the block. The water is turned back through
180 degrees by the block and then exits through an orifice with an area of 120 cm2 . Draw a
suitably annotated control volume and surface and show the inlet and outlet conditions for
this problem. First, find the velocity Ve of the water exiting the block. Second, determine
the force Fx required to hold the block in place. Hint: Assume one-dimensional flow and no
losses.